Question: Simplify the following expression: $a = \dfrac{z^2 + 12z + 35}{z + 7} $
Solution: First factor the polynomial in the numerator. $ z^2 + 12z + 35 = (z + 7)(z + 5) $ So we can rewrite the expression as: $a = \dfrac{(z + 7)(z + 5)}{z + 7} $ We can divide the numerator and denominator by $(z + 7)$ on condition that $z \neq -7$ Therefore $a = z + 5; z \neq -7$